Levinson微梁谐振器热弹性阻尼的广义热弹耦合分析  

Generalized thermoelastic coupling analysis of thermoelastic damping of Levinson micro beam resonator

作　　者：张志超 曹静 高配峰 ZHANG Zhi-chao;CAO Jing;GAO Pei-feng(School of Civil Science and Engineering,Yangzhou University,Yangzhou 225127,China;College of Civil Engineering and Mechanics,Lanzhou University,Lanzhou 730000,China)

机构地区：[1]扬州大学建筑科学与工程学院,江苏扬州225127 [2]兰州大学土木工程与力学学院,甘肃兰州730000

出　　处：《振动工程学报》2023年第1期76-85,共10页Journal of Vibration Engineering

基　　金：江苏省基础研究计划青年项目(BK20180894);国家自然科学基金青年项目(12102380)。

摘　　要：本文基于Levinson梁理论和单向耦合的非傅里叶热传导理论,在不同边界条件下研究了均匀微梁的热弹性阻尼(thermoelastic damping,TED)。忽略温度的轴向梯度引起的热流,给出了Levinson微梁横向自由振动的热弹性耦合微分方程,与微梁不考虑热弹性阻尼时的自由振动方程进行比较,从方程形式的相似性上得到了复频率的解析解,进而求得了代表微梁结构热弹性阻尼的逆品质因子。在此基础上,采用有限元方法计算了微梁结构考虑非傅里叶热传导时的逆品质因子,并将有限元结果和理论分析结果进行了对比验证。通过数值计算结果定量分析了微梁的几何尺寸、边界条件以及频率阶数对微梁热弹性阻尼的影响规律。计算结果表明:在不同频率阶数时,微梁的热弹性阻尼最大值不变,临界厚度均随着频率阶数的增大而减小;不同边界条件下微梁热弹性阻尼最大值对应的临界厚度随着支座约束刚度的增大而减小;忽略轴向的温度梯度引起的热流,在梁尺寸较小时会带来一定误差。Based on Levinson beam theory and unidirectional coupled non-Fourier heat conduction theory,the thermoelastic damp⁃ing(TED)of uniform micro beams with different boundary conditions was studied.Neglecting the heat flow caused by the axial gradient of temperature,the differential equation of free vibration of Levinson micro-beam was given.According to the similarity of equation forms,the analytical solution of characteristic frequency is obtained,and then the inverse quality factor representing the TED of micro-beam structure was obtained.Then,the inverse quality factor of the micro beam structure considering the non-Fourier heat conduction was calculated by the finite element method,and the finite element results are compared with the theoreti⁃cal analysis results.Based on the numerical results,the influence of the geometric size,boundary conditions and vibration mode of the micro-beam on the TED were analyzed quantitatively.The results show that:when the micro-beam vibrates at different fre⁃quency orders,the maximum value of TED remains unchanged and the critical thickness decrease with the increase of the order of vibration mode;Under different boundary conditions,the critical thickness corresponding to the maximum TED of the micro-beam decreases with the increase of the constraint stiffness of the support;Ignoring the heat flux caused by the axial temperature gradient will bring some errors when the beam size is small.

关 键 词：自由振动 微梁 热弹性阻尼 非傅里叶热传导 

分 类 号：O326[理学—一般力学与力学基础]